The advantage of subdomains is that they allow you to have multiple Web sites or to use multiple servers without having to purchase additional domain names.
Answering your specific questions:
1. Not necessarily. Unless you heavily cross-link these subdomains (and risk looking spammy to the search engines), they will be seen to exist as separate sites.
2. Generally, you'd have content (a Web site) on your main domain or on its "www" subdomain, and you'd define and use the other subdomains only if you actually needed them. Examples of "need" might be, a test subdomain where you can test a new version of your site before going live, a mobile subdomain with special content for cell phones and PDAs with limited screen size and multimedia-handling capability, etc.
3. Use your main domain or its "www" subdomain for your main site. Delete the other subdoamins from your DNS zone file if you don't use them for something meaningful. If you choose to use your "www" subdomain for your main site, then 301-redirect the main domain to that subdomain. If you choose to use the non-www domain for your main site, then 301-redirect the "www" to that main domain.
Basically, you do not want the same content to be available at more that one unique URL. If you allow the same content to appear at multiple URLs, then these URLs will essentially 'compete' against each other for search engine ranking, lowering the ranking of all. To avoid this, make sure that any non-canonical URLs are redirected to the canonical URL for each resource, and get this done before your site becomes 'important' to you in any way; It is much easier to prevent problems now that it is to clean them up later.
There are many threads here on URL canonicalization and duplicate-content problems, especially in the Google Search News forum -- Check out the threads cited in the Google Hot Topics thread pinned at the top of that forum for a lot more information on these and other subjects.